Start by dropping your first token on any empty square.
From then on place the next piece on a position orthogonally adjacent to your previous Token in such a way that you change direction in each step.

The last 30 Tokens you put down are specially colored. This makes it easier for you to see where you have gone in recent moves.
The newest Token is always coloured white, the previous light yellow and so on.

You win if you manage to cover all 125 positions.

Once you managed to win, start on a different position next time.

Variant 2: same as variant 1, but with different board graphics.
Variants 3 and 4 are much easier: here you walk through a 4x4x4 cube.
Variant 5: 2x5x5 block
Variant 6: 4x5x5 block
The solution to variants 4,5,6 are attached.

Please note there are two alternative piece sets available, especially designed for the new board graphics in variant 2 and 4 !.

 
Cubewalk is based on a real puzzle I designed in 1986, consisting of 125 little cubes all connected by an elastic string which turned 90 degrees inside each cube. I produced only a dozen or so by hand.
 
Long before 1985 I once had analyzed which boxes a x b x c in general allow such a zigzag walk which covers all cubicles of the box. (Note that the 3x3x3 cube does NOT have a solution!) The article covering my results was titled 'Which blocks are snakes?'. I sent it to JORM (Journal of Recreational Mathematics), but I don't know whether it was ever published.
 
Thanks to Dan Troyka for allowing me to derive my board design from his Superstring board.
 
 
More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz.